(i)[3]
Apply the substitution $x = t^2 + 1$ to show that $I = \int_1^5 (2x - 2) \ln x\,dx$.
(ii)[5]
Hence calculate the exact value of $I$.
Mathematics 9709 · AS & A Level · Integration
Integration — practice question
The integral $I$ is given by $I = \int_0^2 4t^3 \ln(t^2 + 1)\,dt$.